My bad. I did not know that. Won’t make that mistake again. Pasting below the key info.

Differential Growth and L-systems are both concepts used in modeling biological growth, particularly in plants, but they approach the subject from different angles.

Differential Growth

Definition: Differential growth refers to the varying rates of growth in different parts of an organism, leading to shape formation and structural changes. This concept is crucial in understanding how plants adapt their forms in response to environmental stimuli (like light and gravity) and internal signals (like hormones).

Mechanism: It involves the controlled distribution of growth factors and varying growth rates among different tissues. For example, in plants, differential growth can lead to bending or twisting of stems and leaves, as seen in the formation of the apical hook during germination12.

Applications: This concept is used in various fields, including biology, architecture, and design, to create models that simulate how structures grow and change over time3.

L-systems (Lindenmayer Systems)

Definition: L-systems are a mathematical formalism introduced by Aristid Lindenmayer in 1968 for modeling the growth processes of plants. They use a set of rules (productions) to rewrite strings of symbols, which can represent different parts of a plant.

Mechanism: An L-system starts with an initial string (axiom) and applies production rules to generate new strings iteratively. These strings can be interpreted graphically to create complex plant structures. L-systems can be context-free or context-sensitive, allowing for a wide variety of growth patterns45.

Applications: L-systems are widely used in computer graphics for simulating plant growth, generating fractals, and even in architectural design6.

Differential L-systems

Integration: Recent developments have combined differential growth principles with L-systems, known as differential L-systems. This approach allows for more realistic simulations of plant growth by incorporating the effects of differential growth rates into the L-system framework78.

Functionality: In differential L-systems, the growth rules can depend on local conditions, such as the density of neighboring structures or external environmental factors, enhancing the realism of the generated models46.

Summary

Differential Growth focuses on how different parts of an organism grow at different rates due to various factors, leading to complex shapes.

L-systems provide a rule-based framework for simulating plant growth through string rewriting.

The combination of both concepts in differential L-systems allows for advanced modeling that captures both the structural complexity and the dynamic nature of biological growth.

References

[1] Differential growth and shape formation in plant organs www.ncbi.nlm.nih.gov

[2] A Model of Differential Growth-Guided Apical Hook Formation in Plants www.ncbi.nlm.nih.gov

[3] Interactive differential growth simulation for design - GitHub Pages em-yu.github.io

[4] (PDF) Modeling Growth with L-Systems & Mathematica www.researchgate.net

[5] Modeling plant development with L-systems - Algorithmic Botany algorithmicbotany.org

[6] [PDF] L-systems and partial differential equations∗ - Algorithmic Botany algorithmicbotany.org

[7] Differential L-Systems Part 1 | Houdini 20 - YouTube www.youtube.com

[8] Differential L-Systems Part 2 | Houdini 20 - YouTube www.youtube.com